A sum of money amounts to X 2240 at 4% per annum simple interest in 3 yr. The interest on the same sum for 6 months at 3.5% per annum is

Options

A. X30
B. X50
C. X35
D. X150

Answer

To solve the problem, we need to find the principal amount (the original sum of money) first, and then calculate the interest for 6 months at 3.5% per annum.

### Step 1: Calculate the Principal Amount

We know that the amount (A) after 3 years is given as X 2240, and the rate of interest (R) is 4% per annum. The formula for the amount in simple interest is:

\[ A = P + I \]

Where:
- \( A \) = Total amount after time period
- \( P \) = Principal amount
- \( I \) = Simple interest

The simple interest (I) can be calculated using the formula:

\[ I = \frac{P \times R \times T}{100} \]

Where:
- \( R \) = Rate of interest
- \( T \) = Time in years

Substituting the values we know into the formula for interest:

\[ I = \frac{P \times 4 \times 3}{100} = \frac{12P}{100} = 0.12P \]

Now substituting \( I \) back into the amount formula:

\[ A = P + I \]
\[ 2240 = P + 0.12P \]
\[ 2240 = 1.12P \]

Now, solve for \( P \):

\[ P = \frac{2240}{1.12} \]

Calculating \( P \):

\[ P = 2000 \]

### Step 2: Calculate the Interest for 6 Months at 3.5% Per Annum

Now that we have the principal amount (P = 2000), we can calculate the interest for 6 months at a rate of 3.5% per annum.

Since 6 months is half a year, we can use the simple interest formula again:

\[ I = \frac{P \times R \times T}{100} \]

Where:
- \( R = 3.5 \)
- \( T = 0.5 \) (for 6 months)

Substituting the values:

\[ I = \frac{2000 \times 3.5 \times 0.5}{100} \]

Calculating \( I \):

\[ I = \frac{2000 \times 3.5 \times 0.5}{100} = \frac{3500}{100} = 35 \]

### Final Answer

The interest on the same sum for 6 months at 3.5% per annum is **X 35**.

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